pith. machine review for the scientific record. sign in

arxiv: 2605.10982 · v1 · submitted 2026-05-09 · 🌀 gr-qc

Recognition: 3 theorem links

· Lean Theorem

Anisotropic Cosmology with interacting Dark Energy in f(R,T) Gravity: A Data-Constrained & independent Approach

S. H. Shekh , N. Myrzakulov , Anirudh Pradhan , M. Zeyauddin
Authors on Pith no claims yet

Pith reviewed 2026-05-13 00:44 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(R,T) gravityBianchi type Ianisotropic cosmologyvariable deceleration parameterdark energyHubble dataPantheon+ supernovaeobservational constraints
0
0 comments X

The pith

A variable deceleration parameter in f(R,T) gravity yields an anisotropic model consistent with supernova and Hubble observations.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops a model for an expanding anisotropic universe using f(R,T) gravity that incorporates both dark matter and dark energy. It employs a phenomenological variable deceleration parameter to reconstruct the Hubble expansion rate as a function of redshift. The parameters of this model are constrained using observational Hubble data and the Pantheon+ compilation of Type Ia supernovae. The resulting cosmology shows a transition to accelerated expansion consistent with current data and approaches a de Sitter-like state in the future, with late-time behavior similar to the standard model.

Core claim

The paper establishes that inserting a specific phenomenological form of the variable deceleration parameter into the field equations of f(R,T) gravity for a Bianchi type-I metric produces a Hubble function whose free parameters are tightly constrained by current cosmological datasets, successfully reproducing the decelerating-to-accelerating transition and asymptotic approach to de Sitter expansion while satisfying energy conditions.

What carries the argument

Variable deceleration parameter q(z) used to derive the redshift-dependent Hubble function H(z) in the context of f(R,T) modified gravity applied to anisotropic Bianchi-I spacetime.

If this is right

  • The model transitions from an early decelerating phase to the current accelerated epoch.
  • It asymptotically approaches a de Sitter-like regime.
  • Geometrical diagnostics including statefinder and Om indicate close correspondence with ΛCDM at late times.
  • The effective equation of state suggests a quintessence-like dark energy component.
  • Energy conditions are satisfied, confirming physical admissibility.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Small residual anisotropy at late times could be tested with future precision surveys.
  • The reported perturbative instabilities suggest the need for further stability analysis in modified gravity models.
  • Similar reconstruction techniques might apply to other gravity theories for comparative studies of dark energy.

Load-bearing premise

That the chosen phenomenological form of the variable deceleration parameter produces a Hubble function whose parameters can be constrained by Hubble and supernova data without introducing significant systematics or circular reasoning.

What would settle it

Observational data showing a significantly different transition redshift from deceleration to acceleration or a failure to constrain the model parameters within the reported bounds would falsify the reconstruction scheme.

Figures

Figures reproduced from arXiv: 2605.10982 by Anirudh Pradhan, M. Zeyauddin, N. Myrzakulov, S. H. Shekh.

Figure 1
Figure 1. Figure 1: FIG. 1. One-dimensional marginalized distributions and two [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Comparison of the model with [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The behavior of [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The behavior of [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The behavior of [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The behavior of [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Evolution of the squared sound speed [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Evolution of the energy conditions as a function of red [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
read the original abstract

In this work, we investigate the cosmological dynamics of an anisotropic Universe within the framework of $f(R,T)$ gravity by incorporating pressureless dark matter and the dark energy models. The analysis is carried out in a Bianchi type-I space-time, allowing us to capture possible deviations from isotropy and their evolution during cosmic expansion. A phenomenological reconstruction scheme based on a variable deceleration parameter is adopted to derive a redshift-dependent Hubble function. To establish observational viability, we constrain the free parameters of the model using a comprehensive statistical analysis that combines observational Hubble data and the Pantheon+ Type Ia supernova compilation. The resulting parameter space is tightly bounded, and the reconstructed expansion history exhibits strong consistency with current observational expectations. The model successfully reproduces the transition from an early decelerating phase to the present accelerated epoch, while asymptotically approaching a de Sitter-like regime. Further we analyzed the geometrical diagnostics, including the statefinder and $O_m$ diagnostics, which indicate a close correspondence with the standard $\Lambda$CDM scenario at late times. The behavior of the effective equation of state suggests a dynamically evolving dark energy component consistent with a quintessence-like regime. Additionally, the analysis of energy conditions confirms the physical admissibility of the model, whereas the stability investigation reveals the presence of classical instabilities at the perturbative level.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript investigates anisotropic cosmology in f(R,T) gravity with interacting dark energy in a Bianchi-I spacetime. It adopts a phenomenological variable deceleration parameter q(z) to reconstruct a redshift-dependent Hubble function, constrains the free parameters via a statistical fit to observational Hubble data and the Pantheon+ Type Ia supernova compilation, and reports tight bounds, consistency with observations, a deceleration-to-acceleration transition, asymptotic de Sitter behavior, plus analyses of statefinder, Om diagnostics, effective equation of state, energy conditions, and perturbative stability.

Significance. If the Hubble reconstruction were shown to be independent of the q(z) ansatz, the work would offer a concrete example of data-constrained anisotropic modified-gravity models, with the multi-diagnostic analysis and dual data sets providing a useful template for viability checks. The reported late-time approach to Lambda-CDM-like behavior and quintessence-like equation of state would then constitute a non-trivial consistency test.

major comments (2)
  1. [Abstract] Abstract and reconstruction scheme: the Hubble function is obtained by inserting an assumed redshift-dependent deceleration parameter q(z) into the f(R,T) field equations for the Bianchi-I metric; the coefficients of this q(z) are then fitted to the same OHD + Pantheon+ data used to claim observational viability and tight bounds. This procedure makes the reported consistency with the deceleration-to-acceleration transition and de Sitter asymptote largely a validation of the chosen phenomenological form rather than an independent test of the f(R,T) dynamics or the dark-energy interaction term.
  2. [Abstract] Abstract and § (reconstruction): no explicit derivation steps, error budgets, or covariance matrices are supplied for how the f(R,T) equations plus interaction term translate the q(z) ansatz into the final H(z) expression whose two free parameters are constrained; without these, it is impossible to assess whether the model parameters inside f(R,T) and the interaction are genuinely constrained or are effectively absorbed into the q(z) fit.
minor comments (2)
  1. The title's claim of a 'Data-Constrained & independent Approach' should be qualified or justified once the role of the q(z) ansatz is clarified.
  2. Figure captions and tables should explicitly state the priors, best-fit values, and 1-sigma uncertainties for all free parameters (q(z) coefficients, f(R,T) parameters, interaction strength) to allow direct comparison with Lambda-CDM.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report on our manuscript. Below we provide point-by-point responses to the major comments, along with indications of the revisions we will implement.

read point-by-point responses

  1. Referee: [Abstract] Abstract and reconstruction scheme: the Hubble function is obtained by inserting an assumed redshift-dependent deceleration parameter q(z) into the f(R,T) field equations for the Bianchi-I metric; the coefficients of this q(z) are then fitted to the same OHD + Pantheon+ data used to claim observational viability and tight bounds. This procedure makes the reported consistency with the deceleration-to-acceleration transition and de Sitter asymptote largely a validation of the chosen phenomenological form rather than an independent test of the f(R,T) dynamics or the dark-energy interaction term.

    Authors: We thank the referee for highlighting this important aspect of our methodology. Our reconstruction indeed relies on a phenomenological variable deceleration parameter q(z) to obtain the Hubble function within the f(R,T) gravity framework. This is a deliberate choice to enable a data-driven exploration of the model, consistent with approaches used in similar studies of modified gravity cosmologies. The f(R,T) dynamics and the dark energy interaction are integral to deriving the consistent expansion history, and the multi-diagnostic analysis provides additional checks on the model's behavior. We will revise the abstract and the relevant sections to emphasize the phenomenological character of the reconstruction and to clarify that the observational consistency is achieved within this ansatz-based approach. revision: yes

  2. Referee: [Abstract] Abstract and § (reconstruction): no explicit derivation steps, error budgets, or covariance matrices are supplied for how the f(R,T) equations plus interaction term translate the q(z) ansatz into the final H(z) expression whose two free parameters are constrained; without these, it is impossible to assess whether the model parameters inside f(R,T) and the interaction are genuinely constrained or are effectively absorbed into the q(z) fit.

    Authors: We acknowledge the omission of detailed derivation steps in the submitted manuscript. In the revised version, we will include a comprehensive derivation outlining how the f(R,T) field equations for the Bianchi-I spacetime, together with the interaction term, lead to the reconstructed H(z) from the q(z) ansatz. Furthermore, we will supply the error budgets for the parameter constraints and discuss the covariance matrix obtained from the statistical analysis of the OHD and Pantheon+ data. This will help clarify the role of the f(R,T) and interaction parameters in the model. revision: yes

Circularity Check

1 steps flagged

Phenomenological q(z) form dictates H(z) and transition; fit to OHD+Pantheon+ validates input ansatz rather than f(R,T) dynamics

specific steps
  1. fitted input called prediction [Abstract (reconstruction scheme)]
    "A phenomenological reconstruction scheme based on a variable deceleration parameter is adopted to derive a redshift-dependent Hubble function. To establish observational viability, we constrain the free parameters of the model using a comprehensive statistical analysis that combines observational Hubble data and the Pantheon+ Type Ia supernova compilation. The resulting parameter space is tightly bounded, and the reconstructed expansion history exhibits strong consistency with current observational expectations. The model successfully reproduces the transition from an early decelerating phase."

    The variable q(z) is inserted by hand as a phenomenological form whose coefficients directly control the deceleration-to-acceleration transition and de Sitter limit. H(z) follows immediately from the kinematic definition q = -1 - Ḣ/H² (or its redshift equivalent), so the two free parameters of H(z) are identical to those of the assumed q(z). Fitting those parameters to OHD + Pantheon+ therefore fits the input ansatz to the data; the subsequent claim that the model 'reproduces the transition' and shows 'strong consistency' is true by construction of the chosen q(z) rather than an independent output of the f(R,T) equations or the dark-energy interaction.

full rationale

The paper's reconstruction begins with an explicit phenomenological assumption for the deceleration parameter q(z) that already encodes the required early deceleration, late acceleration, and de Sitter asymptote. The Hubble function is then obtained from the standard kinematic identity relating q and H; its two free parameters are subsequently fitted to the same Hubble and supernova data used to assert consistency. Because the transition and asymptotic behavior are built into the chosen q(z) parametrization, the reported tight bounds and 'strong consistency' reduce to a statistical fit of that ansatz. The f(R,T) field equations and interaction term are applied after the fact to interpret the kinematics but do not independently generate the expansion history. This constitutes a fitted-input-called-prediction circularity at the core of the observational viability claim, though the modified-gravity sector itself may still contain non-circular content once H(z) is fixed.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on a phenomenological ansatz for the deceleration parameter and on the validity of the f(R,T) field equations in an anisotropic metric; both are taken from the literature without new justification.

free parameters (2)
  • coefficients of the variable deceleration parameter
    Chosen to produce a redshift-dependent Hubble function that is then fitted to observations.
  • model parameters inside f(R,T) and the dark-energy interaction term
    Adjusted via statistical analysis to match Hubble and Pantheon+ data.
axioms (2)
  • domain assumption Bianchi type-I metric is an adequate description of possible late-time anisotropy
    Invoked to capture deviations from isotropy without further justification in the abstract.
  • domain assumption f(R,T) gravity provides the correct effective field equations for the coupled dark sector
    Standard assumption of the modified-gravity framework used throughout.

pith-pipeline@v0.9.0 · 5553 in / 1670 out tokens · 38748 ms · 2026-05-13T00:44:18.139802+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

68 extracted references · 68 canonical work pages

  1. [1]

    Stability analysis: squared sound speed To assess the physical viability of the reconstructed cosmological scenario, we examine its classical stability by analyzing the response of the cosmic fluid to small perturbations. A key quantity in this context is the squared sound speed, denoted byϑ 2, which character- izes the propagation of perturbations and is...

    work page

  2. [2]

    Energy conditions The physical acceptability of the model can be tested by examining the energy conditions in terms of the re- constructed pressure and energy density. a. Null Energy Condition (NEC) ρs +p s ≥0. (55) Using Eqs. (29) and (30), we find ρs +p s =−ρ m + 2(λ1 +λ 2) 16π+3λ 2 2 ˙H+6H 2 . (56) b. Weak Energy Condition (WEC) ρs ≥0,ρ s +p s ≥0. (57)...

    work page

  3. [3]

    A. G. Riess et al., Astron. J.116, 1009 (1998)

    work page 1998

  4. [4]

    Perlmutter et al., Astrophys

    S. Perlmutter et al., Astrophys. J.517, 565 (1999)

    work page 1999

  5. [5]

    D. N. Spergel et al., Astrophys. J. Suppl.148, 175 (2003)

    work page 2003

  6. [6]

    Astrophys.641, A6 (2020)

    N Aghanim et al., Astron. Astrophys.641, A6 (2020)

    work page 2020

  7. [7]

    D. J. Eisenstein et al., Astrophys. J.633, 560 (2005)

    work page 2005

  8. [8]

    Weinberg, Rev

    S. Weinberg, Rev. Mod. Phys.61, 1 (1989)

    work page 1989

  9. [9]

    S. M. Carroll, Living Rev. Relativ.4, 1 (2001)

    work page 2001

  10. [10]

    Ratra and P

    B. Ratra and P . J. E. Peebles, Phys. Rev. D37, 3406 (1988)

    work page 1988

  11. [11]

    R. R. Caldwell, R. Dave and P . J. Steinhardt, Phys. Rev. Lett.80, 1582 (1998)

    work page 1998

  12. [12]

    R. R. Caldwell, Phys. Lett. B545, 23 (2002)

    work page 2002

  13. [13]

    Z. K. Guo et al., Phys. Lett. B608, 177 (2005)

    work page 2005

  14. [14]

    Armendariz-Picon et al., Phys

    C. Armendariz-Picon et al., Phys. Rev. D63, 103510 (2001)

    work page 2001

  15. [15]

    Nojiri and S

    S. Nojiri and S. D. Odintsov, Phys. Rev. D74, 086005 (2006)

    work page 2006

  16. [16]

    Capozziello et al., Phys

    S. Capozziello et al., Phys. Lett. B639, 135 (2006)

    work page 2006

  17. [17]

    Nojiri and S

    S. Nojiri and S. D. Odintsov, Phys. Lett. B631, 1 (2005)

    work page 2005

  18. [18]

    Harko et al., Phys

    T. Harko et al., Phys. Rev. D84, 024020 (2011)

    work page 2011

  19. [19]

    Singh, A

    K. Singh, A. K. Yadav and V . K. Bhardwaj, Astrophys. Space Sci. (2025)

    work page 2025

  20. [20]

    Kumar, S

    R. Kumar, S. K. Tripathy and P . Sahoo, Eur. Phys. J. Plus (2025)

    work page 2025

  21. [21]

    Hernandez-Almada, M

    A. Hernandez-Almada, M. A. Garcia-Aspeitia and J. Maga˜na, Eur. Phys. J. C (2024)

    work page 2024

  22. [22]

    Sharif and A

    M. Sharif and A. Waseem, Astropart. Phys. (2025)

    work page 2025

  23. [23]

    Bahamonde, et al., Eur

    S. Bahamonde, et al., Eur. Phys. J. C (2024)

    work page 2024

  24. [24]

    Wormhole solutions inf(R,T) gravity,

    P . H. R. S. Moraes, et al., “Wormhole solutions inf(R,T) gravity,” Universe7, 43 (2024)

    work page 2024

  25. [25]

    Shabani and M

    H. Shabani and M. Farhoudi, Phys. Rev. D90, 044031 (2014)

    work page 2014

  26. [26]

    F. G. Alvarenga et al., JCAP1309, 007 (2013)

    work page 2013

  27. [27]

    Dimensional Reduction in Quantum Gravity

    G. ’t Hooft, arXiv:gr-qc/9310026

    work page Pith review arXiv

  28. [28]

    Susskind, J

    L. Susskind, J. Math. Phys.36, 6377 (1995)

    work page 1995

  29. [29]

    Li, Phys

    M. Li, Phys. Lett. B603, 1 (2004)

    work page 2004

  30. [30]

    Tavayef et al., Phys

    M. Tavayef et al., Phys. Lett. B781, 195 (2018)

    work page 2018

  31. [31]

    Moradpour et al., Eur

    H. Moradpour et al., Eur. Phys. J. C78, 829 (2018)

    work page 2018

  32. [32]

    A. S. Jahromi et al., Phys. Lett. B780, 21 (2018)

    work page 2018

  33. [33]

    G. F. R. Ellis, J. Math. Phys.10, 1451 (1969)

    work page 1969

  34. [34]

    C. B. Collins and S. W. Hawking, Astrophys. J.180, 317 (1973)

    work page 1973

  35. [35]

    M. S. Berman, A special law of variation for Hubble’s pa- rameter,Nuovo Cimento B74, 182 (1983)

    work page 1983

  36. [36]

    Abdussattar and R. G. Vishwakarma,Classical and Quan- tum Gravity14, 945 (1997)

    work page 1997

  37. [37]

    Pradhan and H

    A. Pradhan and H. Amirhashchi,Modern Physics Letters A 26, 2261 (2011)

    work page 2011

  38. [38]

    Sahni, T

    V . Sahni, T. D. Saini, A. A. Starobinsky, and U. Alam,JETP Letters77, 201 (2003)

    work page 2003

  39. [39]

    Shafieloo,Mon

    A. Shafieloo,Mon. Not. R. Astron. Soc.380, 1573 (2007)

    work page 2007

  40. [40]

    Moresco et al.,Astrophys

    M. Moresco et al.,Astrophys. J.898, 82 (2020)

    work page 2020

  41. [41]

    Farooq, et al., Astrophys

    O. Farooq, et al., Astrophys. J.,835, 026 (2017)

    work page 2017

  42. [42]

    Moresco, A

    M. Moresco, A. Cimatti, R. Jimenez et al., J. Cosm. As- tropart. Phys.,1208, 006 (2012)

    work page 2012

  43. [43]

    Zhang and J

    M.-J. Zhang and J. -Q. Xia, J. Cosm. Astropart. Phys.,12, 005 (2016)

    work page 2016

  44. [44]

    Blake, et al., Mon

    C. Blake, et al., Mon. Not. Roy. Astron. Soc.,425, 405 (2012)

    work page 2012

  45. [45]

    Simon, L

    J. Simon, L. Verde and R. Jimenez, Phys. Rev. D71, 123001 (2005)

    work page 2005

  46. [46]

    Stern, R

    D. Stern, R. Jimenez, L. Verde, et al. J. Cosm. Astropart. Phys.,1002, 008 (2010)

    work page 2010

  47. [47]

    A. L. Ratsimbazafy, S. I. Loubser, S. M. Crawford, et al., Mon. Not. Roy. Astron. Soc.,467, 3239 (2017)

    work page 2017

  48. [48]

    Gaztanaga, E., et al. Mon. Not. Roy. Astron. Soc.,399, 1663 (2009)

    work page 2009

  49. [49]

    Moresco, M., Mon. Not. Roy. Astron. Soc.,450, L16 (2015)

    work page 2015

  50. [50]

    S. Alam, M. Ata, S. Bailey et al., Mon. Not. Roy. Astron. Soc.470, 2617 (2017)

    work page 2017

  51. [51]

    Moresco, L

    M. Moresco, L. Pozzetti, A. Cimatti et al., J. Cosm. As- tropart. Phys.,1605, 014 (2016)

    work page 2016

  52. [52]

    Delubac, J

    T. Delubac, J. F. Bautista, N. G. Busca, et al., Astron. As- trophys.,574, A59 (2015)

    work page 2015

  53. [53]

    Font-Ribera, D

    A. Font-Ribera, D. Kirkby, N. Busca, et al., J. Cosmol. As- tropart. Phys.,05, 027 (2014)

    work page 2014

  54. [54]

    Wang, et al., Mon

    Y. Wang, et al., Mon. Not. Roy. Astron. Soc.,469, 3762 (2017)

    work page 2017

  55. [55]

    Two new di- agnostics of dark energy,

    V .Sahni, A.Shafieloo, and A.A.Starobinsky, “Two new di- agnostics of dark energy,” Phys. Rev. D78, 103502 (2008)

    work page 2008

  56. [56]

    Shafieloo et al., Is cosmic acceleration slowing down?, Phys

    A. Shafieloo et al., Is cosmic acceleration slowing down?, Phys. Rev. D, (2009), 80, (083528)

    work page 2009

  57. [57]

    D. M. Scolnic et al.,Astrophys. J.859, 101 (2018)

    work page 2018

  58. [58]

    R. R. Caldwell,Phys. Lett. B545, 23 (2002)

    work page 2002

  59. [59]

    Sami and S

    M. Sami and S. Toporensky,Mod. Phys. Lett. A19, 1509 (2004)

    work page 2004

  60. [60]

    Elizalde, S

    E. Elizalde, S. Nojiri and S. D. Odintsov,Phys. Rev. D70, 043539 (2004)

    work page 2004

  61. [61]

    Nojiri and S

    S. Nojiri and S. D. Odintsov,Phys. Lett. B562, 147 (2003)

    work page 2003

  62. [62]

    Armendariz-Picon, V

    C. Armendariz-Picon, V . Mukhanov and P . J. Steinhardt, Phys. Rev. Lett.85, 4438 (2000). 16 TABLE II. Compilation of 77 observational Hubble parameterH(z)measurements (in km s −1Mpc−1). Method I: Cosmic Chronometers, II: BAO (galaxy), III: BAO (Lyα). S.Noz H(z)Method Ref S.Noz H(z)Method Ref 1 0.00 69.1±1.3 I [39] 40 0.68 93.9±8.1 I [40] 2 0.07 70.4±20 I...

    work page 2000

  63. [63]

    Padmanabhan,Phys

    T. Padmanabhan,Phys. Rev. D66, 021301 (2002)

    work page 2002

  64. [64]

    Khoury and A

    J. Khoury and A. Weltman,Phys. Rev. D69, 044026 (2004)

    work page 2004

  65. [65]

    M. C. Bento, O. Bertolami and A. A. Sen,Phys. Rev. D66, 043507 (2002)

    work page 2002

  66. [66]

    Zarrouki and M

    R. Zarrouki and M. Bennai,Int. J. Mod. Phys. A25, 2507 (2010)

    work page 2010

  67. [67]

    Hinshaw et al.,Astrophys

    G. Hinshaw et al.,Astrophys. J. Suppl. Ser.208, 19 (2023)

    work page 2023

  68. [68]

    P . A. R. Ade et al.,Astron. Astrophys.594, A13 (2015)

    work page 2015